Whisk lime juice, yogurt, tandoori powder, salt, and pepper in a bowl. Pour mixture into a resealable plastic bag. Add chicken, coat with the marinade, squeeze out excess air, and seal the bag. Marinate in refrigerator for at least 2 hours.

Preheat an outdoor grill for medium-high heat, and lightly oil the grate.

Remove chicken from the bag and transfer to a plate or baking sheet lined with paper towels. Pat chicken pieces dry with more paper towels.

Grill chicken on the preheated grill with the lid open for 2 minutes. Close lid and continue to grill chicken for 6 minutes.

Turn chicken, close lid and grill until well-browned and meat is no longer pink in the center, about 6 minutes. An instant-read thermometer inserted into the thickest part of the thigh should read 180 degrees F (82 degrees C).